Question: Simplify the following expression: $ p = \dfrac{r - 3}{r + 6} + \dfrac{1}{8} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{8}{8}$ $ \dfrac{r - 3}{r + 6} \times \dfrac{8}{8} = \dfrac{8r - 24}{8r + 48} $ Multiply the second expression by $\dfrac{r + 6}{r + 6}$ $ \dfrac{1}{8} \times \dfrac{r + 6}{r + 6} = \dfrac{r + 6}{8r + 48} $ Therefore $ p = \dfrac{8r - 24}{8r + 48} + \dfrac{r + 6}{8r + 48} $ Now the expressions have the same denominator we can simply add the numerators: $p = \dfrac{8r - 24 + r + 6}{8r + 48} $ $p = \dfrac{9r - 18}{8r + 48}$